Brady, 34, has pleaded not guilty to attacking Rehma Sabir in her Cambridge home. Authorities say Brady was in sole care of the child on the day she suffered massive head trauma. She died two days later, on Jan. 16.

At the hearing in Cambridge District Court, a judge granted Thompson’s motion to preserve some evidence, including the Sabir family’s computer, the child’s medical records since birth, and the family’s travel itinerary in the months before her death.

Brady, a native of Ireland who has been living in the country illegally, attended the hearing but hid from view. She is being held on $500,000 bail.

Investigators found blood-stained baby wipes in the child’s bedroom and a blood-stained pillow and blanket in her crib, prosecutors have said.

A preliminary autopsy found that Rehma had preexisting injuries: bone fractures that appeared to be between two weeks and two months old. Thompson has noted that the family took the child on two extensive trips overseas before the attack.

Prosecutors say they may charge Brady with murder once the autopsy is finished. There is no timetable for its completion, a spokeswoman for the district attorney handling the case said Friday.